On the domain structure of thin ferromagnetic films

The energy of Bloch walls is calculated for very thin ferromagnetic films with respect to the demagnetizing energy of a Bloch wall. A model of the stability of the domain structure in thin films is proposed.Part of this paper was delivered at the conference of solid state physics in Sopoty (Poland) November 5–11th, 1956.     

Fluctuation description of the phase transition from a homogeneous magnetization state to domain structure in thin ferromagnetic films induced by film thickness change

It is revealed that fluctuations of the vector of magnetization in a homogeneous magnetization state have domain-like character. It manifests as well in formulae describing the energy of fluctuation as in the shape of correlation functions. The condition of fluctuation energy positive determination allows to obtain analytic formulae describing critical the thickness L_c of thin films and period λ of the domain structure appearing when L = L_c. The difficulties connected with interpretation of the obtained results in the formalism of the scaling theory are discussed.     

Experimental investigation of the magnetic structure of domain walls in thin ferromagnetic films

The structure of domain walls in thin magnetic films has been studied by the Lorentz method using electron microscopy. The possible existence of the coinciding and opposite directions of rotation of the magnetization vector in Néel domain walls has been proved experimentally. The domain walls separating 90° domains have been found in single-crystal magnetic films. These walls consist of domains with a considerably smaller area than 90° domains.     

The effect of stripe domain structure on dynamic permeability of thin ferromagnetic films with out-of-plane uniaxial anisotropy

The permeability is calculated for a thin ferromagnetic film with the stripe domain structure and out-of-plane uniaxial magnetic anisotropy. Analytical expressions for the frequency dependence of components of permeability tensor are derived with the use of the Smit–Beljers method, with the thickness of domain walls and the domain wall motion being neglected. The effect of the domain width and the angle between the anisotropy axis and the film plane on the frequency dependence of the permeability is analyzed. General equations relating the static permeability components and the ferromagnetic resonance frequencies are found. The results of the approach are applied to the derivation of the constraint for the microwave permeability of thin ferromagnetic films. The analysis of the constraint as a function of the axis deviation angle, the domain aspect ratio and the damping parameter allows the conditions to be found for maximal microwave permeability. The results obtained may be useful in connection with the problem of developing high-permeable microwave magnetic materials.     

Model for domain wall avalanches in ferromagnetic thin films

The Barkhausen jumps or avalanches in magnetic domain-walls motion between successive pinned configurations, due the competition among magnetic external driving force and substrum quenched disorder, appear in bulk materials and thin films. We introduce a model based in rules for the domain wall evolution of ferromagnetic media with exchange or short-range interactions, that include disorder and driving force effects. We simulate in 2-dimensions with Monte Carlo dynamics, calculate numerically distributions of sizes and durations of the jumps and find power-law critical behavior. The avalanche-size exponent is in excellent agreement with experimental results for thin films and is close to predictions of the other models, such as like random-field and random-bond disorder, or functional renormalization group. The model allows us to review current issues in the study of avalanches motion of the magnetic domain walls in thin films with ferromagnetic interactions and opens a new approach to describe these materials with dipolar or long-range interactions.     

Asymmetry in the dynamics of domain walls in thin exchange-coupled ferromagnetic films

The kinetics of remagnetization after magnetic field switching was studied by the magneto-optic visualization technique in the bilayer hybrid structure composed of exchange-coupled FeNi and FeMn films. It was observed that not only the static but the dynamic characteristics of remagnetization as well depend on the polarity of a field applied along the direction of easy magnetization. The rate of the process was found to be exponentially dependent on the field strength in both directions, but the rate varied by factors of 10 upon inversion of the field. It was shown that this difference is the consequence of variation of both the time of domains nucleation and the velocity of domain walls motion.     

Suppression of the domain structure in uniaxial ferromagnetic films with a superconducting coating

Specific models of domain walls are used to investigate conditions for the single-domain state and quasi-single-domain states in structures with magnetic materials having a quality factor higher than one. It is shown that the critical thickness of the magnetic film in a tangentially magnetized system decreases monotonically as the magnetizing field increases from zero to the transition from the collinear to the homogeneous angular phase and then increases monotonically with increasing external field. In a thin isolated magnetic film, the size of the domains increases exponentially with decreasing thickness. This dependence is logarithmic near the transition to the single-domain state for a film coated on two sides and obeys a power law for a film coated on one side. The establishment of a single-domain state and characteristic features in the asymptotic behavior of the domain structure in magnetic films with and without coatings can be attributed to differences in the asymptotic behavior of the field of a single domain wall. Fiz. Tverd. Tela (St. Petersburg) 40, 1068–1074 (June 1998)     

Domain structure and magnetization reversal in thin ferromagnetic elinvar films

A study was made of single-layer Fe-Ni-Cr Elinvar films ranging in thickness from 400 to 10,000 Å and prepared by the thermal sputtering process. For the first time the domain structure of these alloys was examined and found to vary depending on the technological process conditions as well as on the film thickness. The coercive force H is shown here as a function of the specimen thickness, with a maximum value H = 32 Oe in a 640 Å film. The hysteresis loop of Elinvar films has uniaxial anisotropy.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii Fizika, No. 11, pp. 114–117, November, 1971.     

Amorphization of biperiodic domain structures in quasi-uniaxial magnetic films with a critical thickness

The behavior of biperiodic stripe domain structures in quasi-uniaxial magnetic films with a near-critical thickness is studied by scanning magnetic force microscopy and magnetooptical diffraction. In these films, antiphase and hybrid biperiodic domain structures are found to be absent, and the phase transitions between monoperiodic and in-phase biperiodic domain structures are shown to proceed through two-dimensional domain arrays that are amorphized in the arrangement of near-surface distortions in the domain-wall profile.     

Magnetooptic setup for investigating the dynamic properties of domain walls in thin ferromagnetic films

A magnetooptic Kerr setup is designed for investigating the dynamic properties of domain walls in thin ferromagnetic films subjected to an external magnetic field in the temperature range 20–150°C. With this setup, the method of interrupted magnetization is implemented and the magnetic (domain) structure is visualized based on the meridional Kerr effect. The domain structure is displayed on a PC monitor using a Nikon DXM 1200 high-resolution digital video camera. A dedicated software makes it possible to automatize measurements and data processing.     

Visualization of the domain structure of ferromagnetic films using the magnetochemical effect

Iron film surfaces have been studied after their chemical treatment in a magnetic field. The chemical treatment of a metal leads to the appearance of a relief image that is interpreted as a “photograph” of magnetic scattering fields. The morphology of the relief image formed is shown to correlate with the domain structure of a magnetic film. The magnetochemical effect revealed allows the visualization of the dependence of the scattering field distribution at the sample surface on external magnetic field.     

Thickness dependence of the Curie temperature and critical concentration in diluted ferromagnetic thin films

A thickness-dependent critical concentration of an Ising ferromagnetic thin film is predicted. The calculated values of the Curie temperature are bounded by those known for diluted two- and three-dimensional ferromagnets.     

Flexoelectricity induced increase of critical thickness in epitaxial ferroelectric thin films

Flexoelectricity describes the coupling between polarization and strain/stress gradients in insulating crystals. In this paper, using the Landau–Ginsburg–Devonshire phenomenological approach, we found that flexoelectricity could increase the theoretical critical thickness in epitaxial BaTiO₃ thin films, below which the switchable spontaneous polarization vanishes. This increase is remarkable in tensile films while trivial in compressive films due to the electrostriction caused decrease of potential barrier, which can be easily destroyed by the flexoelectricity, between the ferroelectric state and the paraelectric state in tensile films. In addition, the films are still in a uni-polar state even below the critical thickness due to the flexoelectric effect.     

Study of the kinetics of domain structures in thin ferromagnetic films by the Wang-Landau method

The features of a phase transition between the strict striped domain structure in thin ferromagnetic films with transverse anisotropy and the so-called tetragonal phase, where domains can be twisted and broken into parts, have been analyzed. It has been shown that the phase transition should be thermodynamically treated as a Kosterlitz-Thouless transition, where ends of domains serve as vortices. It has been demonstrated with the Wang-Landau numerical algorithm that the kinetics of this phase transition is strongly slowed down owing to the existence of a large number of metastable states; in this property, the system is partially similar to spin glasses.     

Nernst-Ettingshausen effect in thin ferromagnetic films

A new thermomagnetic effect in a ferromagnetic film is discussed. When a temperature gradient is established along the x axis in a ferromagnetic sample, a transverse electric field arises in the same plane as the spontaneous-magnetization vector (in the case H = 0, where H is the external magnetic field). A phenomenological expression is given for the transverse electric field as a function of the square of the magnetization. Theory is given for the Nernst-Ettingshausen effect due to the spin-orbit interaction in a ferromagnetic film in the effectivemass approximation, and the Nernst-Ettingshausen constant is derived. The calculation is carried out by the density-matrix method derived by Kohn and Luttinger.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii Fizika, No. 11, pp. 28–32, November, 1969.     

Dipolar interactions in ferromagnetic thin films

We introduce a discrete model describing the motion of a zigzag domain wall in a disordered ferromagnet with in-plane magnetization, driven by an external magnetic field. The main ingredients are dipolar interactions and anisotropy. We investigate the dynamic hysteresis by analyzing the effects of external field frequency on the coercive field by Monte Carlo simulations. Our results are in good agreement with experiments on Fe/GaAs films reported in literature, and we conclude that dynamic hysteresis in this case can be explained by a single propagating domain wall model without invoking domain nucleation.     

Magnetic anisotropy in thin ferromagnetic films

The magnetic properties of thin ferromagnetic films are studied taking into account the magnetic anisotropy term in the Hamiltonian. In the second approximation equations are obtained for the magnetization of the monatomic layers parallel to the surface of the thin film. From these equations one obtains the Curie temperature, which depends on the thickness of the thin film and the ratio a between the anisotropy constant and the exchange energy between two neighbours. A value can be chosen for such that the thin film becomes ferromagnetic only for a thickness greater than a definite value and in this manner the theoretical results can be fitted to the experimental data. The situation in cobalt thin films is dealt with in particular.

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The author extends his thanks to the research workers of CIFA 1 as well as to Dr. L. Valenta for information on the same subject.     

Magnons in surface-rearranged ferromagnetic thin films

By a Green function approach, spin waves in a surface-rearranged ferromagnetic thin film are derived both analytically and numerically. Heisenberg exchange, bulk and surface anisotropy between nearest neighbors and external magnetic field are taken into account for an sc film with {001} surfaces. Because of the anisotropies, the dynamical matrix defined from the Green function equations is not Hermitian, so we generalize the Bogoliubov canonical transformation to derive the spin wave spectrum. The spin waves propagating inside the film result from the superposition of two sine or hyperbolic sine waves. The amplitude and polarization of spin waves are shown to be quite sensitive to the details of the surface rearrangements, whereas spin wave energies are not so sensitive to such rerrangements, except when soft modes occur in the unrearranged configuration. In that case, we show that when the surface rearrangement is taken into account, soft modes disappear in the spin wave spectrum.     

On the theory of ferromagnetic thin films

As is known, the second approximation in the calculation of the partition function by the traces method of ferromagnetic thin films gives wrong results for the coordination number equal to eight. In order to obtain correct results even for this case, the third order approximation of the partition function is developed and thus the magnetic properties of body-centred cubic iron thin films are studied. The dependence of the Curie temperature on the thickness, for different values of the ratio between the anisotropy constant and the exchange energy between two neighbours, is discussed. A value can be chosen for this ratio such that the thin film becomes ferromagnetic only for a thickness greater than a definite value.

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Influence of ferromagnetic thickness on dynamic anisotropy in exchange-biased MnIr/FeCo multilayered thin films

A comprehensive study of the influence of ferromagnetic thickness on the static and dynamic magnetic properties in exchange-biased FeCo/MnIr multilayers for both strong and weak exchange-bias coupling cases is presented. The results demonstrate that static and dynamic magnetic anisotropy fields decrease with ferromagnetic thickness in both cases. The rising of rotational anisotropy is discussed in conjunction with the enhanced coercivity and exchange bias by taking into account the roles of the rotatable and frozen antiferromagnetic spins in each of the two cases. Due to the contributions of the exchange bias and rotational anisotropy, the resonance frequency can be tailored up to 10 GHz. In addition, the behaviors of the frequency linewidth and the effective damping factor are discussed and ascribed to the dispersion of magnetic anisotropy.